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We develop the first model for extreme mass-ratio inspirals (EMRIs) withmisaligned angular momentum and primary spin, and zero eccentricity -- alsoknown as quasi-spherical inspirals -- evolving under the influence of thefirst-order in mass ratio gravitational self-force. The forcing terms areprovided by an efficient spectral interpolation of the first-ordergravitational self-force in the outgoing radiation gauge. In order to speed upthe calculation of the inspiral we apply a near-identity (averaging)transformation to eliminate all dependence of the orbital phases from theequations of motion while maintaining all secular effects of the first-ordergravitational self-force at post-adiabatic order. The resulting solutions aredefined with respect to `Mino time' so we perform a second averagingtransformation so the inspiral is parametrized in terms of Boyer-Lindquisttime, which is more convenient of LISA data analysis. We also perform a similaranalysis using the two-timescale expansion and find that using either approachyields self-forced inspirals that can be evolved to sub-radian accuracy in lessthan a second. The dominant contribution to the inspiral phase comes from theadiabatic contributions and so we further refine our self-force model usinginformation from gravitational wave flux calculations. The significantdephasing we observe between the lower and higher accuracy models highlightsthe importance of accurately capturing adiabatic contributions to the phaseevolution.

Self-forced inspirals with spin-orbit precession